Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - Scopus: 4A Close Look at Newton–cotes Integration Rules(Cankaya University, 2019) Sermutlu, E.; Sermutlu, Emre; MatematikNewton–Cotes integration rules are the simplest methods in numerical integration. The main advantage of using these rules in quadrature software is ease of programming. In practice, only the lower orders are implemented or tested, because of the negative coefficients of higher orders. Most textbooks state it is not necessary to go beyond Boole’s 5-point rule. Explicit coefficients and error terms for higher orders are seldom given literature. Higher-order rules include negative coefficients therefore roundoff error increases while truncation error decreases as we increase the number of points. But is the optimal one really Simpson or Boole? In this paper, we list coefficients up to 19-points for both open and closed rules, derive the error terms using an elementary and intuitive method, and test the rules on a battery of functions to find the optimum all-round one. © 2019, Cankaya University. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 4A New Quadrature Routine for Improper and Oscillatory Integrals(Elsevier Science inc, 2007) Eyyuboglu, H. T.; Sermutlu, E.In MATLAB environment, a new quadrature routine based on Gaussian quadrature rule has been developed. Its performance is evaluated for improper integrals, rapidly oscillating functions and other types of functions requiring a. large number of evaluations. This performance is compared against the other quadrature routines written for MATLAB in terms of capability, accuracy and computation time. It is found that our routine rates quite favourably. (c) 2006 Elsevier Inc. All rights reserved.Article Citation - WoS: 6Citation - Scopus: 9Comparison of Newton-Cotes and Gaussian Methods of Quadrature(Elsevier Science inc, 2005) Sermutlu, EWe compare Newton-Cotes and Gauss methods of various orders. We give two MATLAB programs that evaluates integrals numerically for given order with given number of points. We make extensive tests with various functions and intervals using same number of points for each method and compare errors. (c) 2005 Elsevier Inc. All rights reserved.